We prove that any Parseval wavelet frame is the projection of an orthonormal wavelet basis for a representation of the Baumslag-Solitar group BS(1, 2) = 〈u, t | utu = t〉. We give a precise description of this representation in some special cases, and show that for wavelet sets, it is related to symbolic dynamics (Theorem 3.14). We show that the structure of the representation depends on the ana...

The supercell- based orthonormal basis method is proposed to investigate the modal properties of the Bragg fibers. A square lattice is constructed by the whole Bragg fiber which is considered as a supercell, and the periodical dielectric structure of the square lattice is decomposed using periodic functions (cosine). The modal electric field is expanded as the sum of the orthonormal set of Herm...

In this paper, an overview about the identification of dynamic systems using orthonormal basis function models, such as those based on Laguerre and Kautz functions, is presented. The mathematical foundations of these models as well as their advantages and limitations are discussed within the contexts of linear, robust, and nonlinear identification. The discussions comprise a broad bibliographic...

A real symmetric matrix is diagonalisable by a suitable orthonormal change of basis. The joint approximate diagonalisation problem is to find an orthonormal change of basis which simultaneously diagonalises, or approximately diagonalises, two or more real symmetric matrices. A number of important signal processing problems require the computation of a joint approximate diagonaliser. However, no...

This contribution deals with the problem of structure determination for generalized orthonormal basis models used in system identiication. The model structure is parameterized by a pre-speciied set of poles. Given this structure and experimental data a model can be estimated using linear regression techniques. Since the variance of the estimated model increases with the number of estimated para...